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On the Parameterized Complexity of Biclique Cover and Partition *

Sunil Chandran, Davis Issac, Andreas Karrenbauer
unpublished
In the BicliquePartition problem, we have the additional constraint that each edge should appear in exactly one of the k bicliques.  ...  We build on this kernel and improve the running time for BicliquePartition to O * (2 2k 2 +k log k+k) by exploiting a linear algebraic view on this problem.  ...  On the Parameterized Complexity of Biclique Cover and Partition E(G 2 ) can be covered by 2 log 2 m bicliques in polynomial time by Lemma 12.  ... 
fatcat:bkhuvovfhvhulagr4ifedzp76u

Covering graphs with few complete bipartite subgraphs

Herbert Fleischner, Egbert Mujuni, Daniël Paulusma, Stefan Szeider
2009 Theoretical Computer Science  
Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional  ...  In this paper, we investigate them in the framework of parameterized complexity: do the problems become easier if k is assumed to be small?  ...  The second author's research was supported by International Science Programme (ISP) of Sweden, under the project ''The Eastern African Universities Mathematics Programme (EAUMP).''  ... 
doi:10.1016/j.tcs.2008.12.059 fatcat:ppshskddmbakfj5r2e2pheenb4

Covering Graphs with Few Complete Bipartite Subgraphs [chapter]

Herbert Fleischner, Egbert Mujuni, Daniel Paulusma, Stefan Szeider
2007 Lecture Notes in Computer Science  
In this paper we investigate them in the framework of parameterized complexity: do the problems become easier if k is assumed to be small?  ...  We observe that the Biclique Vertex-Cover and Biclique Vertex-Partition problem are equivalent, since we can always make the bicliques of a biclique vertex-cover disjoint without increasing the size of  ...  Acknowledgment The authors thank Mike Fellows for helpful discussions.  ... 
doi:10.1007/978-3-540-77050-3_28 fatcat:3veh3svmendplpbl6ogtow6hhy

Mod/Resc Parsimony Inference [chapter]

Igor Nor, Danny Hermelin, Sylvain Charlat, Jan Engelstadter, Max Reuter, Olivier Duron, Marie-France Sagot
2010 Lecture Notes in Computer Science  
We show that this is formally equivalent to the Bipartite Biclique Edge Cover problem and derive some complexity results for our problem using this equivalence.  ...  defined operation on these matrices gives back the input.  ...  [8] studied the Bipartite Biclique Edge Cover problem in the context of parameterized complexity.  ... 
doi:10.1007/978-3-642-13509-5_19 fatcat:mt3u524dffgrlhy7cnn6xor7ye

Exact Algorithms for Biclique Coloring

Guilherme Gomes, Carlos Lima, Vinicius dos Santos
2022 Matemática contemporânea  
We present algorithms to determine if a graph has a k-biclique-coloring: an O * (4 n )-time algorithm using exact cover, and an O * (k + 2) 2dtime FPT algorithm, where d is the neighborhood diversity of  ...  A k-biclique-coloring of G is k-coloring of the vertices of G with no maximal monochromatic biclique. A recent work showed that determining if such a coloring exists is Σ P 2 -complete for k > 2.  ...  Since B ∪ {u} is a biclique, Proj(u) is adjacent to only one partition of B ′ .  ... 
doi:10.21711/231766362021/rmc485 fatcat:7edkr5mayzah5bnv3jrmvwbmfa

Exact exponential-time algorithms for finding bicliques

Daniel Binkele-Raible, Henning Fernau, Serge Gaspers, Mathieu Liedloff
2010 Information Processing Letters  
Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques.  ...  The NP-complete problem of finding a non-induced (k 1 , k 2 )-biclique asks to decide whether G contains a non-induced biclique (X, Y ) such that |X| = k 1 and |Y | = k 2 .  ...  We already mentioned that CBVC, the parameterized dual of Non-induced (k 1 , k 2 ) Biclique, is in FPT. It is a natural question to ask whether Non-induced (k 1 , k 2 ) Biclique is in FPT as well.  ... 
doi:10.1016/j.ipl.2010.10.020 fatcat:auug2gskdfelrpykz5mrvyswwm

Efficient Approximation for Restricted Biclique Cover Problems

Alessandro Epasto, Eli Upfal
2018 Algorithms  
The decision version of the minimum biclique cover problem is NP-Complete, and unless P = NP, the cover size cannot be approximated in general within less than a sub-linear factor of the number of nodes  ...  We show that this practical version of the biclique cover problem is amenable to efficient approximations.  ...  The research was partially supported by NSF grant IIS-1247581 and NIH grant R01-CA180776. Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/a11060084 fatcat:mf5haw4krrbyfpgycexkppx3si

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms [article]

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 arXiv   pre-print
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
arXiv:2006.04411v1 fatcat:hjgu7f3s7zbydkcnioq3qlzgza

Preprocessing Subgraph and Minor Problems: When Does a Small Vertex Cover Help? [article]

Fedor V. Fomin and Bart M. P. Jansen and Michal Pilipczuk
2013 arXiv   pre-print
We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph.  ...  While our characterization captures many interesting problems, the kernelization complexity landscape of parameterizations by vertex cover is much more involved.  ...  In parameterized graph algorithms, one of the most important and relevant complexity measures of a graph is its treewidth.  ... 
arXiv:1206.4912v3 fatcat:yady3pi7krfwjajng3z3ni4x3u

A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

Andreas Emil Feldmann, Karthik C. S., Euiwoong Lee, Pasin Manurangsi
2020 Algorithms  
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results.  ...  We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/a13060146 fatcat:2u2vv3uksfguvj6473t2gsq42a

Graph Square Roots of Small Distance from Degree One Graphs [article]

Petr A. Golovach, Paloma T. Lima, Charis Papadopoulos
2020 arXiv   pre-print
We are interested in the parameterized complexity of the problem for classes ℋ that are composed by the graphs at vertex deletion distance at most k from graphs of maximum degree at most one, that is,  ...  We show that different variants of the problems with constraints on the number of isolated vertices and edges in H-S are FPT when parameterized by k by demonstrating algorithms with running time 2^2^O(  ...  Note that if B has a biclique cover of size strictly less than k, we can add arbitrary bicliques to this cover and obtain a biclique cover for B of size exactly k.  ... 
arXiv:2010.05733v1 fatcat:43jifxqrfjcyvjplbcvdejbl4e

Characterizing the easy-to-find subgraphs from the viewpoint of polynomial-time algorithms, kernels, and Turing kernels [chapter]

Bart M. P. Jansen, Dániel Marx
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
if G contains t vertexdisjoint subgraphs isomorphic to H. do not give a complete characterization of the cases when F-Subgraph Test admits polynomial many-one kernels, but show examples that this question  ...  We study two fundamental problems related to finding subgraphs: (1) given graphs G and H, Subgraph Test asks if H is isomorphic to a subgraph of G, (2) given graphs G, H, and an integer t, Packing asks  ...  for the many-one complexity of F-Subgraph Test.  ... 
doi:10.1137/1.9781611973730.42 dblp:conf/soda/JansenM15 fatcat:k67ttnsabjcitiaox6khfgcfpe

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs [article]

Tomohiro Koana, Christian Komusiewicz, Frank Sommer
2020 arXiv   pre-print
Comp. 2020] on clique enumeration, we show that several problems related to finding dense subgraphs, such as the enumeration of bicliques and s-plexes, are fixed-parameter tractable with respect to γ(G  ...  This graph parameter is never larger than the degeneracy (plus one) and can be significantly smaller. Extending the work of Fox et al. [SIAM J.  ...  For more details on parameterized complexity, we refer to the standard monographs [5, 7] . Variants of Independent Set In this section we study Independent Set and related problems.  ... 
arXiv:2007.05630v2 fatcat:woyutwltbzfeflz6yd5j7z4njm

On the Fine-Grained Complexity of Rainbow Coloring

Łukasz Kowalik, Juho Lauri, Arkadiusz Socała
2018 SIAM Journal on Discrete Mathematics  
We show that the problem is FPT when parameterized by q and has a kernel of size O(q) for every k ≥ 2, extending the result of Ananth et al. [FSTTCS 2011].  ...  We believe that our techniques used for the lower bounds may shed some light on the complexity of the classical Edge Coloring problem, where it is a major open question if a 2 O(n) -time algorithm exists  ...  Then the edges ofḠ can be covered by O(p 2 ∆ 1 (G) log n) bicliques fromḠ so that any edge of G and any biclique have at most one common vertex.  ... 
doi:10.1137/16m1102690 fatcat:27emtdloibf3vbpf4ny75mxc4i

A survey on the parameterized complexity of the independent set and (connected) dominating set reconfiguration problems [article]

Nicolas Bousquet and Amer E. Mouawad and Naomi Nishimura and Sebastian Siebertz
2022 arXiv   pre-print
We survey both older and more recent work on the parameterized complexity of all three problems when parameterized by the number of tokens k.  ...  The emphasis will be on positive results and the most common techniques for the design of fixed-parameter tractable algorithms.  ...  We survey both older and more recent work on the parameterized complexity of all three problems when parameterized by the number of tokens k.  ... 
arXiv:2204.10526v1 fatcat:ua3pkqxtabatbbl6jydhy3i3b4
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